Heterogeneous effects of welfare reforms on earnings, transfers and income have been established theoretically and empirically. Welfare reform studies usually focus on average or quantile treatment effects, which depend on the marginal distributions of potential treatment and control outcomes. Less is known about parameters that depend on the joint distribution of potential outcomes, such as quantiles of the distribution of treatment effects. We propose a two-step approach to identify these parameters under the identifying assumption that all permutations producing a given rank correlation between potential treatment and control outcomes are equally likely to occur. We first employ baseline covariates to estimate the rank correlation coefficient between potential treatment and control outcomes. Using this estimate, we then average over permutation-specific unit-level treatment effects to obtain quantiles of the distribution of treatment effects. Rearranging these quantiles yields a generalized version of quantile treatment effects, which do not rely on a rank invariance assumption. Our analysis of experimental data from Connecticut's Jobs First program reveals that the program initially increased incomes of a larger fraction of program participants than previously recognized. Long-term gains and losses caused by the program were about 2-4 times larger than those derived from conventional quantile treatment effects.

Mathias Sinning is an Associate Professor at the Crawford School of Public Policy of the Australian National University (ANU). He is interested in the empirical analysis of issues related to Labor Economics, Public Economics and Policy Evaluation. His current research focuses on the development and application of methods to study treatment response heterogeneity. Ongoing applied work includes the implementation of randomized controlled field trials to study behavioral aspects of tax compliance. His work has been published in Economic Inquiry, Health Economics, Industrial and Labor Relations Review, Journal of Banking and Finance and Journal of Economic Behavior and Organization, among others. Mathias has previously held academic appointments at the ANU and the University of Queensland. He has been a Visiting Fellow of the Office of Population Research at Princeton University and the National School of Development at Peking University.